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Register a new userAtomic decomposition and Weak Factorization for Bergman-Orlicz spaces
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For $mathbb B^n$ the unit ball of $mathbb C^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L^Phi_alpha(mathbb B^n)$, which are generalizations of classical Bergman spaces. We obtain atomic decomposition for functions in the Bergman-Orlicz space $mathcal A^Phi_alpha (mathbb B^n)$ where $Phi$ is either convex or concave growth function. We then prove weak factorization theorems involving the Bloch space and a Bergman-Orlicz space and also weak factorization theorems involving two Bergman-Orlicz spaces.
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In this paper we characterize off-diagonal Carleson embeddings for both Hardy-Orlicz spaces and Bergman-Orlicz spaces of the upper-half plane. We use these results to obtain embedding relations and pointwise multipliers between these spaces.
For $mathbb B^n$ the unit ball of $mathbb C^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L^Phi_alpha$, which are generalizations of classical Bergman spaces. We characterize the dual space of large Bergman-Orlicz space, and bounded Hankel operators between some Bergman-Orlicz spaces $A_alpha^{Phi_1}(mathbb B^n)$ and $A_alpha^{Phi_2}(mathbb B^n)$ where $Phi_1$ and $Phi_2$ are either convex or concave growth functions.
We prove Carleson embeddings for Bergman-Orlicz spaces of the unit ball that extend the lower triangle estimates for the usual Bergman spaces.
We use the method of atomic decomposition to build new families of function spaces, similar to Besov spaces, in measure spaces with grids, a very mild assumption. Besov spaces with low regularity are considered in measure spaces with good grids, and results on multipliers and left compositions are obtained.
We discuss sampling constants for dominating sets in Bergman spaces. Our method is based on a Remez-type inequality by Andrievskii and Ruscheweyh. We also comment on extensions of the method to other spaces such as Fock and Paley-Wiener spaces.
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